I have reservations about using Acts as an historical source and I'm not alone.
The much better informed people at the
Westar Institute seem to think Acts is less than reliable as a source for possible 1st century Christianity.
Their conclusions:
"The Acts Seminar met twice a year beginning in 2001 and concluded its work at the spring Westar meeting in 2011. Dennis Smith, the seminar chair, compiled a list of the top ten accomplishment of the Acts Seminar:
The use of Acts as a source for history has long needed critical reassessment.
Acts was written in the early decades of the second century.
The author of Acts used the letters of Paul as sources.
Except for the letters of Paul, no other historically reliable source can be identified for Acts.
Acts can no longer be considered an independent source for the life and mission of Paul.
Contrary to Acts 1-7, Jerusalem was not the birthplace of Christianity.
Acts constructs its story on the model of epic and related literature.
The author of Acts created names for characters as storytelling devices.
Acts constructs its story to fit ideological goals.
Acts is a primary historical source for second century Christianity."
Obviously, the conclusions they arrived at are not written in stone, but I'm glad to see I'm not alone in thinking Acts is not a go-to source for the 1st century church's practices.
At the end of the day, what I mean to say is that Acts doesn't seem like the best source for learning about what Christians of the first century may or may not have called themselves.